Negadecimal?

Number Theory Level pending

Mary decides to start counting in negadecimal (i.e. base " negative $10$ ").

She starts, " $1, 2, 3, 4, 5, 6, 7, 8, 9, ...$ "

Just then she is interrupted by an important phone call.

Joe decides to continue where she left off...

What will be the next number, where Joe should continue counting?

1 solution

Geoff Pilling
Nov 28, 2016

In base $-10$ , a number is calculated as follows:

$\overline{abc} = a(-10)^2 + b(-10)^1 + c(-10)^0$

So, in this system, $10_{10} = \boxed{190}_{-10}$ where the subscript represents the base of the number.